Measurement Science and Technology
Meas. Sci. Technol. 27 (2016) 097002 (6pp)

doi:10.1088/0957-0233/27/9/097002

Technical Note

Magnetic field sensor usinga polymer-based vibrator
Jiang Wu, Kazuhiko Hasebe, Yosuke Mizuno, Marie Tabaru
and Kentaro Nakamura
Laboratory for Future Interdisciplinary Research of Science and Technology,
Tokyo Institute of Technology, Yokohama 226-8503, Japan
E-mail: wujiang@sonic.pi.titech.ac.jp
Received 29 March 2016, revised 21 June 2016
Accepted for publication 7 July 2016
Published 2 August 2016
Abstract

In this technical note, a polymer-based magnetic sensor with a high resolution was devised forsensing the high magnetic field. It consisted of a bimorph (vibrator) made of poly (phenylene
sulfide) (PPS) and a phosphor-bronze foil glued on the free end of the bimorph. According
to Faraday’s law of induction, when a magnetic field in the direction perpendicular to thebimorph was applied, the foil cut the magnetic flux, and generated an alternating voltage
across the leads at the natural frequency of the bimorph. Because PPS has low mechanicalloss, low elastic modulus, and low density, high vibration velocity can be achieved if it isemployed as the elastomer of the bimorph. The devised sensor was tested in the magnetic
field range of 0.1–570 mT and exhibited a minimum detectable magnetic field of 0.1 mT. At azero-to-peak driving voltage of 60 V, the sensitivity of the PPS-based magnetic sensor reached10.5 V T−1, which was 1.36 times the value of the aluminum-based magnetic sensor with thesame principle and dimensions.
Keywords: poly (phenylene sulfide), polymer-based vibrator, bimorph,
Faraday’s law of induction, magnetic field sensor(Some figures may appear in colour only in the online journal)

1. Introduction

1/f noise restricts their resolution [1, 10]. The newly-invented
magnetosensitive materials, e.g. magnetoresistive, magnetostrictive, magnetoelectric, and magnetooptical materials, areeffective in magnetic field sensing [11–18]. However, theirperformance is greatly influenced by the synthesis technology[1, 14, 15], which is under intensive investigation to achieve
the practical usage of the magnetosensitive materials.
Magnetic fields can be measured based on electromagnetic
principles. To date, a variety of magnetometers with dimensions in the order of several hundred micrometers have beensuccessfully fabricated with the microelectromechanical system (MEMS) technology [17–19]. Most of the MEMS magnetometers operated on the basis of the Lorentz force, andemployed the cantilever as the basic structure: when a cur­rent flowed along the cantilever, the applied magnetic field

High magnetic field sensing, or low sensitivity field sensing,is the technique for measuring a magnetic field greater than
the geomagnetic field [1, 2]. It has a variety of applications,e.g. magnetic memory readout and high-current measurement[1, 3, 4]. Recently, the magnetic sensor having a wide dynamic
range and high resolution has been increasingly in demand forthe precise sensing of the high magnetic field. Semiconductorbased magnetic sensors, e.g. the Hall-effect sensors, are widelyused owing to their small size and low price [5–9]1, but their
sensitivity is limited within a small range [6, 7]. Besides, the1

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Meas. Sci. Technol. 27 (2016) 097002

generated the Lorentz force, which led to a deformation of thecantilever. The deformation was measured from the variationin the capacity formed between the deformed cantilever andthe static part. This sensor provided a direct-current (DC) output, and its resolution was restricted by the 1/f noise.
To raise the signal-to-noise ratio, a method that provides
an alternating-current (AC) signal as the output is employed.
According to Faraday’s law of induction, an AC voltage is
generated on a conductive bar vibrating vertically to a static
magnetic field. Our research group has devised several kindsof magnetic field sensors with thin piezoelectric ceramic elements [20]. Longitudinal vibration or extensional vibration
was used in these sensors. A part of the electrode plated on thepiezo­electric ceramic element was used as the sensing wire,
while the rest of the electrode was employed for applying an
AC voltage to drive the vibration at the mechanical resonancefrequency. In this work, bimorph, which is a cantilever sandwiched by two piezoelectric ceramic plates, was employed as
the basic structure of the magnetic field sensor, because it hasa relatively simple structure and high vibration velocity compared to the previously tested vibrators. The material of thevibrating body has a great influence on the performance ofthe sensor. The previously tested vibrator had a piezoelectricceramic vibrating body, and its maximum vibration velocity
was limited to 300 mm s−1 due to the fatigue of the piezo­
electric ceramic. Our recent previous research found that poly(phenylene sulfide) (PPS), as a functional polymer, exhibited
low attenuation for ultrasound even in high vibration ampl­
itude range [21–23]. Besides, MEMS processing, e.g. etching, sputtering, and ferroelectric-film deposition, has been
implemented on the flexible organic substrate [24–26], andit indicates that a micro-sized magnetic field sensor may bemade with a PPS elastomer. Currently, silicon is used as thesubstrate in MEMS magnetometers. Because of the high elastic modulus and the small dimensions, the cantilever provided
an extremely low deformation, resulting in low sensitivity ofthe silicon-based MEMS sensor. If PPS replaces silicon as thesubstrate, the sensitivity of the magnetic field sensor can bemarkedly increased.
As a preliminary study of the micro-sized polymer-basedmagnetic field sensor, we fabricate a PPS-based magnetic
field sensor with the dimensions of several dozen millimeters,
and test its basic performance. The devised sensor operates on
the basis of Faraday’s law of induction, which is totally different from the principle of the aforementioned sensors (theLorentz force), though they have the same basic structure, thecantilever.

a cylindrical head (10 mm in diameter and 5 mm in length).
One end of the rectangular part was fixed. Two piezoelectric
ceramic plates (C213, Fuji Ceramics, Fujinomiya, Japan)
10 mm in length, 6 mm in width, and 0.5 mm in thickness,were glued onto the surface of the rectangle part of the elastomer to excite the bending vibration in the direction parallelto the z-axis.
(2) Sensing part: at the free end of the bimorph, a phosphor-bronze foil 20 mm in length, 2 mm in width, and 0.1 mm
in thickness, was glued along the x-axis. When there is a uniform magnetic field along the y-axis, an output voltage u is
induced between the leads:u = Blv,
(1)where B, l, and v represent the magnetic flux density, the foil
length, and the vibration velocity at the free end, respectively.
In this work, we employed a low-mechanical-loss polymer, PPS, as the elastomer. Its elastic modulus and density are
3.45 GPa and 1350 kg m−3, respectively. The damping coefficient measured in air was 0.002 [21–23]. Because the vibration velocity is inversely proportional to the product of thedamping factor and the square root of the elastic modulus anddensity [27], PPS is a suitable material to obtain a high vibration velocity, which results in high sensitivity of the magnetic
sensor.
In this work, we connected the foil and the signal conditioning circuit with a 0.3 mm diameter wire, which was alsoa candidate as the sensing material. It is easier to glue thefoil onto the bimorph than the thin wires, because the foil
provides a relatively large surface. Thus, we used the foil as
the sensing material in this work. Coils are commonly usedin the magnetic field sensors to increase the interlinking [11].
However, the sensitivity cannot be increased unless the coilis partially shielded from the magnetic field due to the working principle of this sensor. In figure 2(a), the voltage, u,
induced from a single foil (wire) equals the product of themagnetic flux density, B, the foil length, l, and the vibration
velocity, v. Figures 2(b) and (c) shows a rectangular spiralcoil and a helix coil, respectively. In the spiral coil shown infigure 2(b), if we define that the electric potential at P1 is 0,
the electric potential at P2 equals Blv. Since P1P2 and P3P4
have the same vibration velocity, v, they yield the voltagesof Blv and Bl1v, respectively. Thus, the electric potential at
P4 decreases to (Blv  −  Bl1v), which is in proportion to thelength change along the x-axis, (l  −  l1). Similarly, the electric
potential at P8 is Bv[(l  −  l1)  +  (l2  −  l3)]. The output voltageof the spiral coil equals Blv, the same as the output of the foil
in figure 2(a). In the helix coil (figure 2(c)), the induced volt­age of PIPII equals the value of PIVPIII. As can be observed,
the helix yields an output voltage of Blv, which is independent of the number of turns. If some foils are parallelly fixed
on the bimorph and connected by the leads shielded fromthe magn­etic field, the sensitivity is increased (figure 2(d)),
but the sensing system becomes complicated. The vibration
velocity becomes low if the foil and the magnetic shielding
component are tightly connected. Thus, the unshielded leadneeds to be carefully arranged to decrease its negative effecton the vibration performance.

2. Materials and methods
Figure 1 shows the schematic and dimensions of the magnetic
field sensor, which consisted of an exciting part and sensing
part:(1) Exciting part: the bimorph was composed of an elastomer and two rectangle piezoelectric ceramic elements.
The PPS-based elastomer was divided into a rectangular part
(45 mm in length, 10 mm in width, and 3 mm in thickness) and2

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Meas. Sci. Technol. 27 (2016) 097002

Figure 1. Magnetic field sensor with a PPS-based bimorph: (a) its schematic and dimensions and (b) a picture of the prototype.

Figure 2. Output voltage induced by (a) a metal plate or wire, (b) a rectangular spiral coil, (c) a rectangular helix coil, and (d) parallel coils
connected with magnetic-shielded leads.

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Meas. Sci. Technol. 27 (2016) 097002

Figure 3. Experimental setup for measuring the magnetic field.

3. Measurement system

4. Experimental results

Figure 3 shows the experimental setup. The bimorph was
driven by a high-intensity AC signal at its natural frequency.
The leads were twisted to decrease the mutual inductive coupling between the exciting and sensing circuits. Magnetic
fields in the ranges of 0.1–12.5 mT and 12.5–570 mT weregenerated with a Helmholtz coil and a neodymium magnet,
respectively. The Helmholtz coil was electrically connected
to a DC power supply. When a DC voltage was applied, auniform magnetic field of 0.1–12.5 mT was generated inside
the coil, and its density was adjusted by changing the current.
The Helmholtz coil was composed of two parallel coils 25 mm
in length and 60 mm in diameter. The foil was placed at thecenter of the coil. For calibration, the magnetic flux density at
the location of the foil was recorded versus the current using
a Hall-effect sensor (A1324, Allegro, Worcester, U.S.). The
magnetic field of 12.5–570 mT was generated with a 20 mm
diameter 20 mm long neodymium magnet and its density was
adjusted by changing the position of the magnet along they-axis. Using a magnetometer (6010, TOYO, Tokyo, Japan),the magnetic flux density was measured as a function of thez-axis position. Since the magnetic field generated by the neodymium magnet was non-uniform, at a certain position along
the y-axis, we measured magnetic flux densities along thex-axis in the range from −10 to 10 mm with an interval of
1 mm. The average value was selected as the magnetic flux
density at this position. The leads were electrically connectedto the foil edges using the conductive epoxy. The output volt­
age induced from the foil was conditioned with an instrumentation amplifier (INA118, Texas Instruments, Dallas, U.S.)
with a gain of 60 dB. The amplified signal was detected witha lock-in voltage meter (5560, NF Electronic Instruments,
Yokohama, Japan). A laser Doppler velocimeter (NLV1232,
Polytec, Waldbronn, Germany) was employed to measure thevibration velocity at the free end of the bimorph.

First, the optimal frequency was determined. When the zeroto-peak voltage was set to 60 V, the vibration velocity wasmeasured as the driving frequency was swept from 0.01–20 kHz.
Figure 4(a) shows that peaks appeared in the vibration velocity versus frequency curve at driving frequencies of 0.31, 1.79,
5.35, 10.12, and 18.05 kHz, which corresponded to the 1st,
2nd, 3rd, 4th, and 5th bending modes, respectively. In part­icular, at 0.31 kHz, the 1st order bending mode was excitedand the vibration velocity reached 360 mm s−1, which was
higher than the values at other frequencies. The 5th bending
mode yielded a more observable response than the 3rd and 4th
bending modes, because the piezoelectric ceramic elements
were glued at the place which made it efficient to excite the
5th bending mode. Figure 4(b) shows the voltage depend­ence of the vibration velocity at approximately 0.31 kHz. The
vibration velocity reached 760 mm s−1 at 180 V0-p. The vibration velocity does not increase linearly with increasing driving
voltage, because of the variation in mechanical loss under thehigh vibration amplitude [21].
Figure 5(a) shows the voltage as a function of the magn­
etic flux density at the vibration velocities of 10, 50, 100,
200, and 360 mm s−1. Note that the magnetic flux density on
the abscissa of figure 5(a) does not include the geomagnetic
field. The output voltage increased linearly as the magnetic
flux density was varied from 0.1–570 mT, and the minimum
detectable difference in the magnetic field was 0.1 mT. The
practical range is mainly determined by the input ranges ofthe preamplifier and the lock-in voltmeter. By adjusting thedriving voltage applied to the bimorph, we can easily change
the sensitivity to make the output voltage from the lead suitable for the full scale of the preamplifier and the lock-in volt­age meter. In figure 4(a), the resolution, defined as the ratioof the minimum detectable change to the dynamic range,
reached 0.018%. As mentioned above, this sensor provides

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Meas. Sci. Technol. 27 (2016) 097002

Figure 4. Vibration velocity as functions of (a) frequency at 60 V0-p and (b) driving voltage at approximately 0.31 kHz.

Figure 5. Experimental results: (a) output voltage versus magnetic flux density at vibration velocities of 10, 50, 100, 200, and 360 mm s−1,and (b) sensitivity and offset voltage as a function of vibration velocity.

Clearly, the amplitude had little change, but the phase almost
reversed. The geomagnetic field has a dominant effect on theoffset, while the crosstalk has a minor contribution.
For comparison, we fabricated an aluminum sensor withthe same structure and dimensions as the PPS-based sensor.
The foil was glued onto the aluminum bimorph with electric
insulating epoxy, which can suppress the electrical interference originating from the power supply. At 0.54 kHz, the aluminum sensor yielded a vibration velocity of 266 mm s−1 at
60 V0-p, and had a mechanical quality factor (Q) of 750. The
sensitivity was 7.6 V T−1, which was 0.74 times the value ofthe PPS-based sensor. Although the PPS-based bimorph has
a lower Q factor, it exhibited a larger vibration velocity than
the aluminum bimorph, because PPS had much lower elastic
modulus. In addition, the PPS-based sensor had a weight of
3.2 g, which was 0.55 times the value of the aluminum-based
sensor (5.8 g). These results indicate that the high vibration
velocity (high sensitivity) and the light weight are achieved byutilizing PPS as the bimorph elastomer.
The glass-transition and melting temperature of PPS areapproximately 90 °C and 280 °C, respectively. PPS provides
mechanical-property stability before 90 °C [28]. However, in
the range of 90 °C–280 °C, its elastic modulus has an observable decrease with increasing temperature, which leads to avariation in the resonance frequency. Thus, in practice thean AC voltage, which promises a high signal-to-noise ratio
by applying a lock-in technique. The output voltage versus
magnetic-flux-density curves in figure 5(a) were linearly fitted
and the slope of the fitting line was the sensitivity. Figure 5(b)demonstrates how the sensitivity varied with the vibration
velocity. The sensitivity was 0.3 V T−1 at the vibration velocity of 10 mm s−1 and increased to 10.5 V T−1 linearly as thevibration velocity increased to 360 mm s−1. Since the maximum vibration velocity reaches 760 mm s−1 at 180 V0-p, themaximum sensitivity is expected to be 22 V T−1. The linearity
errors at 10, 50, 100, 200, and 360 mm s−1 were 1.8%, 2.0%,
1.6%, 1.9%, and 1.6%, respectively. The average value was
1.8%, which was at the same level as the values of commercial
magnetic sensors (typically ~1.5%) [5]2.
When the magnetic field was switched off, the magnetic
field sensor yielded a harmonic signal, of which the zero-topeak amplitude was defined as the offset voltage. Figure 5(b)shows that the offset voltage became higher with increasing
vibration velocity. It may be attributed to the geomagnetic field
and the crosstalk between the exciting and sensing circuit. At
20 V0-p, the signal had the amplitude of 0.078 mV and thephase of 53.5°. After the sensor orientation was reversed, its
amplitude and phase were 0.075 mV and  −99.1°, respectively.
2

See footnote 1.
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Meas. Sci. Technol. 27 (2016) 097002

temperature should be  <90 °C. PPS products have a typicalmoisture absorption value of 0.03% at 23 °C for 24 h [28]3.
The value was relatively low among the commonly-used engineering polymers.

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On the basis of Faraday’s law of induction, a magnetic field sensor with a polymer-based vibrator was devised and its basic performance was tested. The output voltage increased linearly as
the magnetic field increased from 0.1–570 mT with a minimum
detectable change of 0.1 mT. Compared with the aluminum
sensor, the polymer-based sensor exhibited relatively high sensitivity and light weight. A sensitivity of 22 V T−1 is expected
when the driving voltage applied to the bimorph reaches 180 V0-p.
With the simple structure and the inherent performance, thismagnetic sensor has the possibility of commercialization if its
dimensions are significantly minimized. In the future, theminiaturization of this sensor will be considered based on
the MEMS technology. In addition, sophisticated design ofthe canti­lever and the pick-up coil will be carried out.
Acknowledgments
The authors are indebted to the Daicel Corporation for providing the functional polymers tested in this work. The authors
also thank Prof. T Shinshi and Assistant Prof W Hijikata, Laboratory for Future Interdisciplinary Research of Science andTechnology, Tokyo Institute of Technology, for their help in
the usage of the magnetometer. This work was partially supported by the Adaptable and Seamless Technology Transfer
Program (A-step, Grant Number AS2711904S) of the Japan
Science and Technology Agency (JST).
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DIC what is PPS: www.dic-global.com/jp/en/products/pps/about.html
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